Chinese Quarterly Journal of Mathematics ›› 2015, Vol. 30 ›› Issue (4): 555-561.doi: 10.13371/j.cnki.chin.q.j.m.2015.04.008

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A New Choice of the Preconditioner of PHSS Method for Saddle Point Problems

  

  1. 1. Department of Mathematics, Shanghai University2. Department of Automotive Engineering, Nanyang Vocational College of Agriculture
  • Received:2014-01-22 Online:2015-12-30 Published:2020-11-19
  • About author:Biographies:WANGShi-heng(1965-), male, native of Nanyang, Henan, an associate professor of Nanyang Vocational College of Agriculture, M.S.D., engages in advanced algebra; WANG Ke(corresponding author)(1978-), male, native of Nanyang, Henan, a lecturer of Shanghai University, Ph.D., engages in numerical linear algebra and scientific computing.
  • Supported by:
    Supported by the National Natural Science Foundation of China(11301330)； Supported by the Shanghai College Teachers Visiting Abroad for Advanced Study Program（B.60-A101-12-010）； Supported by the First-class Discipline of Universities in Shanghai；

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Abstract: Bai, Golub and Pan presented a preconditioned Hermitian and skew-Hermitian splitting（PHSS） method [Numerische Mathematik, 2004, 32: 1-32] for non-Hermitian positive semidefinite linear systems. We improve the method to solve saddle point systems whose（1,1） block is a symmetric positive definite M-matrix with a new choice of the preconditioner and compare it with other preconditioners. The results show that the new preconditioner outperforms the previous ones. 

Key words: saddle point problem, PHSS method, preconditioner

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